Space charge wave amplifiers



July 23, 1957 I PING KING TlEN ETAL 2,800,606

SPACE CHARGE WAVE AMPLIFIERS Filed Oct. 26, 1951 9 F' z i 5 i INPUT I OUTUT D-C POTENTIALY 4r D-CVELOCITY'LL 9 A'C GuRREm'DENsnYCiq 11g. 3.

7 qc V i Q b A-G VELocnYIf y y Q K e I NVENTCR PING KING TIEN w ,1, t LESTRM. FIELD fl/ M ATTORNEY 28%,635 Patented July 23, 1957.

SPACE CHARGE WAVE AMrLnuans Ping King Tien, Stanford, and Lester M. Field, Palo Alto, Calif., assignors to The Board of Trustees of The Leland Stanford Junior University, tanford University, Caliil, a legal entity havir; corporate powers of California Application tltctoher 26, 1951, Serial No. 253,344

ltl Claims. (Cl. 315- 3.6)

One of the principal objects of the invention is to provide electron discharge tubes capable of a high degree of amplification throughout extremely wide bands of microwave frequency spectrum.

Another object is to provide high frequency devices of rugged and simple construction, wherein modulation of an extended electron beam is built up by a succession of changes in D.-C. velocity along the beam.

The invention will be described with reference to the accompanying drawing, wherein:

Fig. l is a schematic diagram of an amplifier embody- 0 ing the invention in a presently preferred form,

Fig. 2 is a graph showing the D.-C. potential distribution along the path of the electron stream in the tube of Fig. 1,

Fig. 3 is a graph of the amplitude of the A.-C. current density in the electron stream as a function of position along the path, corresponding to the potential distribution of Fig. 2, and

Fig. 4 is a graph of the amplitude of the A.-C. velocity of electrons in the stream, corresponding to Figs. 2 and 3. I According to the present invention, the signal to be amplified is impressed on an electron beam to set up plasma oscillations or space charge waves comprising correlated variations of A.-C. current density and A.-C. velocity along the beam. The beam is then decelerated to a relatively low D.-C. or average velocity which may be a small fraction of its initial D.-C. velocity. Then, at a point along the path of the beam when the A.-C. velocity due to the impressed signal is zero, the beam is abruptly accelerated to a relatively high D.-C. velocity, for example that which it had where the signal was applied.

This series of operations on the beam produces a new set of space charge waves like those caused by the input signal, but of substantially greater amplitude. The process may be repeated a number of times on the same beam, if desired, by decelerating the beam and accelerating it again at successive points of zero A.-C. velocity. Each repetition produces a considerable increase in amplitude of the space charge waves, up to the point where the A.-C. ve-

tudinal axis to a collector electrode 3. The gun I may be of known design, comprising a cathode 5, focussing electrode 7, and an anode or accelerator electrode 9. A short conductive helix 11 surrounds the path of the electron beam in the region of the gun 1. A similar helix 13 surrounds the path of the beam near the collector 3. The

initial turn of the helix 11 may be stretched out as shown at 15 to provide a small probe or antenna for coupling to an input wave guide 17. The helix 13 is similarly coupled at 19 to an output guide 21.

The helices 11 and 13 are similar to those used in travelling wave tubes, but they need not be made long enough to produce any substantial amplification. Their purpose is to modulate the beam with an input signal, applied to the guide 17, and to take the amplified'signal oil the beam for transmission by the output guide 21 to utilization means. While it is preferred at present to use helices as shown, other known means may be employed for modulating the beam and extracting oscillatory energy from the beam, for example electrodes such as grids.

A D.-C. source 23 is connected as shown to maintain the accelerator 9 and the helices 11 and 13 at a high positive potential with respect to the cathode 5. This voltage should be such as to accelerate the electrons to a velocity of wave propagation on the helices. The collector 3 may also be held at the accelerator potential. In a typical tube which has been constructed, the helices 11 and 13 were wound of 0.01 inch diameter tungsten wire with a pitch of 26 turns per inch, and an inside diameter of 0.1 inch. These dimensions correspond to an accelerating potential of 2600 volts.

A plurality of apertured conductive disc electrodes 25 27, 33, 35 and 37 surround the path of the electron beam atspaced points between the helices 11 and 13. These electrodes may be provided with short cylindrical rims as shown, for supporting them in alignment withinthe .vacuum envelope 39. The first electrode 25 is disposed adjacent the inner end of the input helix 11, and may be connected thereto. The second electrode 27 is spaced from the first by a distance indicated as D on the drawing. This distance depends upon the conditions under which the tube is designed to operate, and may in a typical case, be about one and three quarters inches. The electrode 27 is connected to a point 29 on the source 23 of relatively low voltage, say about volts. Preferably a voltage divider 31 is included to provide for convenient adjustment of the voltage at the electrode 27.

The third electrode 33 may be connected to the high voltage terminal of the source 23, and is located as' near the electrode 27 as is feasible without the risk of voltage break-down and arcing between the two elements. The electrode 35 is connected like the electrode 27 to the lowvoltage point 29. The separation between electrodes 33 and 35 may be made the same as that between electrodes 25 and 27. The electrode 37 is connected to the high voltage terminal, and is separated from the electrode 35 by a relatively small space, like the distance between the electrodes 27 and 33. The electrode 37 may be connected internally to the end of the output helix 13, as shown.

In the operation of the device, the electron gun 1 proje'cts .a beam of electrons along the axis of the tube, through the helix 11, electrodes 25, 27, 33, 35 and 37, and the helix 13, to the collector 3. The initial D.-C. velocity of the 'beam as it leaves the gun and passes through the helix 11 is relatively high, owing to the high potential of the accelerator 9. As mentioned above, this velocity should be substantially equal to the velocity of Wave propagation along the helix 11, e. g. about one tenth the velocity of light. The terms D.-C. velocity as used herein means the average velocity of the electrons in the part of the stream under consideration, and is designated by the letter u. Cyclical variations in the velocity of electrons passing through a given plane across the stream are referred to as the A.-C. velocity.

in an ideal unmodulated electron stream, all of the electrons move at the D.-C. velocity u, and the electron density or charge density remains constant ata 'D.-C. value, p. Now consider the stream to be sinusoidally if modulated by cyclically accelerating and decelerating'it at some transverse plane. The velocity at this plane is then u+v sin Z'n'fmt, where v is the magnitude of the A.C. velocity and fm is the modulation frequency. As-

sume'ctha't v is much less than u, as isthe case in the. practice of the present invention. As the stream flows on, the electrons which are accelerated will get ahead of their normal or equilibrium positions, and those which-are "decelerated will get behind their equilibriumpositions, so that the stream becomes formed into relativelycom centrated. bunches ofelectrons whiclrare separated by.

rarified regions.

Owingto the mutual repulsionbetween electrons, the

bunches will spread out and coalesce, and the stream will' be of substantially uniform density again-atsomem point along its path. Here the electrons are in. their original equilibrium positions. with :respect to each other,

the axial repulsion forcesexerted on each electron bythose ahead of it being balanced by those behind it. However, the electrons at this. point aremoving with respect to'their equilibrium positions, and momentum carries them past those positions in the opposite directions from those in which they were originally displaced. Thus, the stream is bunched again, at some subsequentpoint, and the cyclerepeats itself.

This phenomenonis called plasma oscillation, or space charge oscillation. The frequency f of oscillation of, the electrons about their equilibrium positions depends upon the restoring force exerted on an electron per unit of its longitudinal displacementfrom equilibrium, and is substantially proportional to the square root of the D.-C. charge density p. The distance through. which the I stream moves at the DC. velocity it during one cycle of versing their directions. of motion with respect to the stream as a whole, i. e. those which have been travelling more slowly, having nearly been overtaken by the bunch are being repelled forward and accelerated, and those faster ones which have nearly overtaken the bunch are repelled in the rearward direction from the bunch. Thus, the A.-C. velocity v at these points is zero, notwithstanding the fact that the stream is modulated. This statement is based on the assumption that the original velocity modulation is small compared to the D.-C. velocity u, so that the electrons do not have enough momentum to overcome the repulsion forces and pass through the bunch. The distance along the stream between consecutive points of zero A.-C. velocity is one half the space charge wavelength, and these points are fixed with respect to the point where the modulation is applied. Midway between these points, the A.-C. velocity is maximum, alternately in the direction of the stream and in the opposite direction. Thus the magnitude of the A.-C. velocity varies periodically as a function of distance along the beam from any fixed reference point, the length of the complete period being one space charge wavelength. This variation of the magnitude of the A.-C. velocity with position along the path of the stream may be regarded as a standing wave, fixed in space.

Where the A.-C. velocity is at a maximum, either positive or negative, the electrons are in their equilibrium positions and therefore the current density is uniform at the D.-C. value q At all other points in the beam the current density will vary at the modulation frequency f above and below q by some amount q. This is the A.-C. current density, and it also varies in magnitude as a function of distance along the beam, being zero where the A.-C. velocity is maximum, and maximum where the A.-C. velocity is zero. Thus, we have a standing wave of A.*C. current density magnitude, correlated with the.A.-C. velocity magnitude wave, and 9 0 degrees out of space phase with it. The amplitudes of these waves are definitely related to each other because all of I the modulation energy is transferred cyclically from one form to the other. I I I The modulation may bra-applied as pure velocity variation, as described above, or as current variation, since.

either one will become converted to the other and back again, producing the same sort of space charge waves.

Furthermore, a mixture of the two kinds of modulation will do the same'thing, the effect being to'start thewaves at :a pointwhere neither isof zero amplitude.

Inthe device of Fig. 1,an inputsignal applied through the'wave guide 17 to'the helix 11 will modulate the electron stream,-in the same manner asin a travelling wave tube. When the beamleavesthe helix, it carries correlated waves of, A.-C. velocity and A.-C., current density due to space charge oscillation, the space charge frequency fp and wavelength h being determined by the D.-C. charge density p and D.-C. velocity u.

The space between the electrodes contains a negative potential gradient, as'indica'ted bythe portion 41 ofthe solid line in the graph of, Fig. ,2. This decelera-tes the electron beam continuouslyduring its passage through the net of the D.-C.' velocity u and the -D.-C; chargedensity p.

space, from the. relatively high velocity corresponding to 2600 volts to the low velocity corresponding to about 75 volts, as indicated by the part 43 of the dash line in Fig. 2. The -D.-C. beam current density q is the same at every point along the beam, assuming all of the electrons stay in the beam, and at each point it is the prod Therefore and the D.-C. charge density must increase uniformly throughout the flow of :the beam inthe deceleration space.

As mentioned above, the plasma frequency fsis 'pro decreases as the three halves power of the velocity. Thus the original set of space charge Waves appearing at the end of the helix 11 are gradually converted in the deceleration space to a new set having a higher plasma frequency and shorter space charge wavelength.

Consider an isolated electron having a D.-C. velocity 11,. The kinetic energy is /2mu Where m is the electron mass. Let the electron be decelerated by passing through a potential drop of V volts. The kinetic energy is then less by the amount Ve, where e is the electron charge, and /zmzz, /2mu =Ve, 11 being the ll-C. velocity after deceleration. Now suppose that besides the D.-C. velocity u,, the electron had a relatively small A.-C. velocity of instantaneous value v,. Then the kinetic energy before deceleration is /2m (u,+v,) and after acceleration is /2m(u,+v,) Thus /2mu, /zmu, (from the above equation).

Collecting the terms and factoring m, this becomes Since v, and v, are small compared to u, and 11,, their squares can be neglected, and u,v,=u v,. The instantaneous A.-C. velocity after deceleration is therefore It is apparent that the new A.-C. velocity is greater than the initial A.-C. velocity, in the same ratio that the original D.-C. velocity is greater than the new D.-C. velocity. I

This process takes place continuously along the beam in the decelerating space, so that the amplitude of the velocity variations at any point along the wave is greater than it would have been at a corresponding point on the wave which would have existed in the absence of deceleration.

Referring to Figs. 3 and 4, it is assumed for generality that the space charge waves at the point a at the end of the helix 11 have a current density amplitude q and velocity amplitude v neither being zero. At some point b in the decelerating space, the A.-C. current density will be zero and the velocity will be at a maximum value v This velocity, owing to the D.-C. deceleration, will be greater than what it would have been at the first point of zero A.-C. current density on a similarly modulated beam which had not been decelerated.

At a subsequent point 0, the A.-C. velocity will be zero and the current density will have a maximum value q likewise greater than what it would have been at a corresponding point of zero velocity on a similar beam,

. not decelerated. Thus the modulation of the beam has been increased by a factor which depends, among other things, upon the difference in voltage between the electrodes 25 and 27. However, the beam velocity u is relatively low, and the DC. charge density p is high.

The distance D between the electrodes 25 and 27 is determined in accordance with the initial beam density and velocity, and the amount by which the beam is to be decelerated, so as to make the current density maximum q occur substantially at the plane of the electrode 27; The distance may be computed analytically, taking into account the fact that the plasma frequency and space charge wavelength differ from their ideal values because the electron stream is of finite cross section. Then correction for small error in the value of D may be made by adjustment of the voltage at the electrode 27 to change the space charge wavelength and make the current density maximum occur there.

The relatively small gap between the electrodes 27 and 33 defines an accelerating space, Where the D.-C. velocity of the beam is abruptly increased to a high value zr which in the present example is the same as the initial value 11,. Since the gap is short compared to a space charge wavelength, the electrons do not have time to change their relative positions appreciably during this acceleration, and the A.-C. current density remains at the same value q The A.-C. velocity, on the other hand, is zero on entering the gap and so is not decreased by the D.-C. acceleration.

Thus, on leaving the gap between electrodes 27 and 33, the beam has the same D.-C. velocity and D.-C. charge density as it had when it left the helix 11, as well as the same kind of modulation. However, the A.-C. current density is much greater than it would have been if the beam had simply travelled at its original D.-C. velocity, and the beam is carrying a new set of space charge waves like that originally started on it by the in put signal, but of larger amplitude, corresponding to max c' The high voltage electrode 33 and low voltage electrode 35 define a second decelerating space, like that between electrodes 25 and 27. The beam is slowed down again in this space reaching an A.-C. current density zero and A.-C. velocity maximum at some point d, and a current density maximum and velocity zero at a subsequent point e. At the point e the beam enters the accelerating gaprbetween the electrodes 35 and 37 and is brought back to its original D.-C. velocity and charge density, without changing the amplitudes of the A.-C. current density and velocity.

After the last acceleration at e, the beam goes through 6 the output helix 13, inducing a wave thereon which gets its energy from the beam modulation and travels to the element 19 and into the output guide 21. Finally the beam strikes the collector electrode 3.

The total gain provided by the amplifier depends upon the structural design, the ratio between -D.-C. velocities at the beginning and end of the decelerating space, and the number of decelerating spaces. The helices 11 and 13 may also contribute some gain, or loss, depending upon their lengths. Although the device described has only two deceleration spaces, any number of such stages may be similarly cascaded along a single beam, each additional stage providing additional gain, up to the point where the modulation of the beam, with a given input signal, becomes so great that small signal conditions no longer obtain. 7

The obtainable gain per stage (i. e. in each decelerating space) is limited by the minimum D.-C. velocity that can be tolerated. As the D.-C. velocity ismade lower, the D.-C. charge density increases, and finally the repulsion forces become so great that the beam flies apart. However, with the dimensions and voltages used in the present example, a gain of about 8 db per stage can be obtained at a frequency of 3000 megacycles per second, with a cathode current of about one milliampere.

In the present stage of the art, the bandwidth of the amplifier is limited principally by that of the terminations, i. e. the coupling means between the helices and the Wave guides. It will be apparent that any known broadband terminations may be used instead of those shown here by way of illustration.

Since many changes could be made in the above construction and many apparently widely different embodiments of this invention could be made Without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1. A space charge wave amplifier including means for producing a modulated electron beam carrying correlated waves of alternating current density and alternating velocity variation having a predetermined space-charge Wavelength, a series of electrodes at spaced points along the beam, means supporting said electrodes and beam producing means in fixed relationship, means connecting electric potentials between said electrodes for defining at least one deceleration space followed by at least one acceleration space, one pair of said series of electrodes defining said one acceleration space being closely spaced and positioned substantially at a point along the beam where the alternating velocity amplitude of said beam due to the modulation thereof is substantially zero, the length of said accelerating space bein. small relative to the spacecharge wavelength of the modulated electron beam.

2. A space charge wave amplifier as set forth in claim 1, wherein said one deceleration space is approximately one half a space charge wavelength long for amplifying said correlated space charge waves along said beam, the location of said one acceleration space along said beam being at a region of maximum variation in current density of the amplified space charge waves with said one acceleration space being considerably shorter than said deceleration space, whereby the alternating current density variation is substantially the same throughout said one acceleration space, said series of electrodes further defining another deceleration space just beyond said acceleration space for further amplifying said space charge waves.

3. A space charge wave amplifier including an input helix and an output helix, said helices being coaxial and longitudinally spaced apart on their common axis, means for producing and directing a beam of electrons along said axis through said input and output helices in succession, terminal means at one end of said input ,helix'for applying an input signal to be amplified tosaid input helix to modulate said electron beam and produce space charge oscillations therein of correlated variations in magnitude of A. C. velocity and A.-C. current density along said beam with said A.-C. velocity magnitude variation being at a minimum and said A.-C. density current magnitude variation being at a maximum at the same points along said beam, and electrode means in the space between said helices defining a deceleration space followed by an acceleration space, the boundary between said deceleration and acceleration spaces being located at a point along said beam where the A.-C. velocity is at a minimum.

4. A space charge wave amplifier comprising means including an electron source for generating a beam of electrons, means positioned adjacent said source for modulating the beam with input signals to 'be amplified, said modulating means producing plasma oscillation of the beam, whereby regions of maximum variation in current density are produced at fixed points along the beam at intervals of a half space-charge wavelength as determined by the beam density and average beam velocity, a plurality of electrodes at spaced points along the beam, means supporting said electrodes and beam generating means in fixed relationship, means connecting electric potentials between said electrodes for defining alternate deceleration spaces and acceleration spaces, the deceleration space being of the order of a half space-charge wavelength of the modulated electron beam, said accelerating spaces being very short relative to said decelerating spaces, and means responsive to modulation of the beam after its passage through said series of spaces to produce an amplified version of said input signals.

5. An electron discharge device comprising means including an electron source for producing a beam of electrons, means positioned adjacent said source for modulating the beam in longitudinal plasma oscillation, the space-charge wavelength of the plasma oscillation being determined by the average charge density and average electron velocity of the beam, a plurality of apertured electrodes, means supporting said electrodes and modulated beam producing means in fixed relationship, the electrodes being positioned in spaced points along the beam, means connecting electric potentials between said electrodes for maintaining alternate ones of said electrodes at relatively high and relatively low potentials, respectively, for alternately decelerating and accelerating the beam in successive regions along the beam, the decelerating space defined by the first two electrodes being of the order of a half space-charge wavelength of the plasma oscillation and the accelerating space between the second and third electrodes being very short compared to the space-charge wavelentgh of the plasma oscillation.

6. A space charge wave amplifier including an electron gun adapted to direct a focused beam of electrons along a substantially linear path, a conductive helix coaxially surrounding a part of said path adjacent said electron gun, and means for supplying high frequency electromagnetic energy which is to be amplified to the end of said helix nearer said gun for exciting plasma oscillation of the beam, said oscillation having a predetermined wavelength as fixed by the average beam density and velocity; a plurality of apertured electrodes surrounding said path at spaced points beyond said helix, the spacings betwee consecutive electrodes being alternately relatively wide and relatively narrow, potential means connected between said widely spaced electrodes for producing a deceleration field therebetween, and potential means connected between the narrowly spaced electrodes for producing an acceleration field therebetween, the distance between said widely spaced electrodes being substantially the order of one half of said wavelength of the plasma oscillation; a second conductive helix coaxially surrounding a part of said path beyond said electrodes, and means for leading amplified Wave energy away from said second helix.

7. In combination, means including a cathode for pro ducing a modulated stream of charged particles along Bil a predetermined path travelling at a first D.-C. velocity and carrying correlated space charge waves of alternating current density variation and alternating velocity variation, the amplitude of said space charge Waves varying according to longitudinal position along the stream to provide stationary patterns of alternating current density amplitude and alternating velocity amplitude which are in 90 space phase relationship to each other, a slow wave propagating structure positioned along said path for interaction with said stream, and means including a pair of electron permeable electrode means spaced along said stream between said cathode and said slow wave propagating structure for changing the D.-C. velocity characteristics of said stream in a predetermined direction along a region between first and second space charge wave alternating velocity minimums for changing the amplitudes of said space charge waves, the first of said pair of electrode means having a conductive portion in close surrounding relationship with said stream, said conductive portion of said first electrode means being located slightly beyond said first space charge wave alternating velocity minimum, the second of said pair of electrode means having a conductive portion in close surrounding relationship with said stream, said conductive portion of said second electrode means being located in the vicinity of said second space charge Wave alternating velocity minimum.

8. The combination as set forth in claim 7, further including third electrode means having a conductive portion in close surrounding relationship with said stream, said conductive portion of said third electrode means being slightly beyond said second space charge wave alternating velocity minimum, said second and third electrode means defining a velocity changing gap short relative to a space charge wavelength for changing the D.-C. velocity characteristics of said stream in a direction opposite said predetermined direction without substantially changing the alternating current density of said space charge waves, and fourth electrode means spaced further along said stream between said third electrode means and helix for further changing the D.-C. velocity characteristics of said stream in said further direction for again changing the amplitudes of said space charge waves in the same direction as said first mentioned change, said fourth electrode means having a conductive portion in close surrounding relationship with said stream, said conductive portion of said fourth electrode means being located in the vicinity of the next succeeding space charge wave alternating velocity minimum from said cathode beyond the minimum at which said second electrode means is located.

9. A space charge wave amplifier, comprising means including a cathode and an electron permeable anode for producing and directing an electron stream having predetermined D.-C. electrical characteristics, means for modulating said stream for carrying correlated space charge standing waves of alternating velocity and alternating current density, the amplitude of said wave of alternating velocity cyclically varying between fixed points of minimum amplitude spaced one half of a space charge wavelength apart along said stream, the amplitude of said wave of alternating current density cyclically varying between fixed points of minimum amplitude spaced one half of a space charge wavelength apart with the amplitude maxima of said alternating current density occurring at the amplitude minima for said wave of alternating velocity, first means for acting upon said stream over a first region along said stream between first and second space charge wave alternating velocity minima for changing said D.-C. electrical characteristics of said stream in a first direction for providing a decrease in space charge wavelength and an increase in the amplitudes of said Waves, second means for acting upon said stream over a second region located further along said stream beyond said first region and in the vicinity of said second alternatingvelocity minimum for providing a further change in the D.-C. electrical characteristics of said stream in an opposite direction from said first change, said second region being short relative to the space charge wavelength whereby there is substantially no change in alternating current density of said beam therealong and substantially no change in the amplitudes of said space charge waves by said second region, and electromagnetic wave energy output means further along said stream beyond said last named means.

10. A space charge wave amplifier as set forth in claim 9, further including third means acting upon said stream between said second means and said wave energy output means over a third region further along said stream between said second alternating velocity minimum and a third alternating velocity minimum for changing said D.-C. electrical characteristics of said stream 10 in said first direction for providing a further increase in the amplitudes of said space charge waves.

References Cited in the file of this patent UNITED STATES PATENTS 2,190,511 Cage Feb. 13, 1940 2,192,049 Metcalf Feb. 27, 1940 2,284,751 Linder June 2, 1942 2,405,611 Samuel Aug. 13, 1946 2,408,809 Pierce Oct. 8, 1946 2,463,267 Hahn Mar. 1, 1949 2,489,082 De Forest Nov. 22, 1949 2,538,267 Pierce et al. Jan. 16, 1951 2,541,843 Tiley Feb. 13, 1951 2,584,597 Landauer Feb. 5, 1952 

